So the application window just disappears, but you don't have to click on the taskbar to get it back, rignt? You just wiggle the mouse and it comes back without clicking on the taskbar? If that's what's happening, I agree it's bizarre. Computers are dumb
machines that unfortunately do bizarre things sometimes, although this is a new one on me. I see no one else has posted a reply here, so it must be a pretty rare thing.
It sounds like you have the antivirus and firewall areas covered. I agree it doesn't sound like a hardware problem, but the only other thing I can think of is possibly some utility that your computer manufacturer might've put on your machines. They like
to do that. I've personally seen that on Dell, HP, and Toshiba PCs as well as other folks' PCs I've helped with from time to time. Apparently your desktop has been doing this since you got it since it's only a week old, but did your 14 month old laptop always
do this or is it something that just happened recently? If it's the latter, you could probably use System Restore to go back to a date prior to the problem.
On the desktop I'd recommend what's called a clean boot where you run
msconfig and disable everything in the startup tab except for your antivirus program to see if that will get around the problem. To run msconfig, click Start and type msconfig in the search box. Then click on msconfig where it shows it and click on
the startup tab. Once there, uncheck everything there except your antivirus program. Then reboot and run that way for long enough to see if the problem's still with you. If it goes away, then you can slowly start adding things back until you find
the culprit.
One other thing you could check would be your screen saver. If you have some custom screen saver, that could be doing it, so you could try changing it to something you know to be part of Windows.
If that doesn't do it, I'm afraid I'm out of ideas, so I wish you good luck!